Estimating the Sizes of Molecules and Atoms
1. Benjamin Franklin wrote:
…at Clapham I observed a large pond very rough with the wind. I fetched out a Cryer of Oil, and dropt a little of it on the water. I saw it spread itself with surprising Swiftness upon the Surface… the Oil tho’ not more than a Tea Spoonful produced an instant calm, over a space several yards square, which spread amazingly, and extended itself gradually … making all that quarter of the Pond, perhaps half an acre, as smooth as a Looking Glass.
Assume for simplicity that the oil molecules are little cubes, what can you conclude about the size of the molecules?
2. From the kinetic theory of gases and the ideal gas law, we deduced a connection between the gas pressure (at some density) and the average molecular speed. We also connected the temperature with the molecular kinetic energy. When Maxwell first analyzed the velocity distribution, he didn't know Boltzmann's constant. Without that knowledge, is there any way these results can be used to guess the size of molecules?
3. Explain how, by carefully matching Planck's formula for black body radiation to the experimentally observed spectrum, it is possible to find Planck's constant. It is also possible to find Boltzmann's constant from the same experimental data. Explain how this could be done, and then show how the mass of an atom could then be deduced from this information and the properties of gases. (Assume you already know the gas constant R.)
4. Brownian Motion. Very tiny particles suspended in a fluid are observed to be in incessant motion. Discuss how observation of this motion, together with the principle of equipartition of energy, could lead to an estimate of Boltzmann's constant, and hence, again, the mass of atoms.
5. In a J. J. Thomson experiment to measure the ratio of charge to mass for cathode rays -- electrons -- electrons accelerated to a kinetic energy of 3000eV
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are directed between two metal plates 1 cm apart and 5 cms long, with a voltage difference of 30V . If the beam enters exactly midway between the plates, moving parallel to them initially, how far off center is it as it leaves the plates? If the beam strikes a screen 25 cms beyond the point of exit from the plates, how far off center is the point of impact? If a uniform magnetic field perpendicular to the paper is applied in the region between the plates, what strength and direction is needed to cause the electron path to be a straight line throughout?
French, Special Relativity, Chapter 6: 17, 19